The plane was carrying 116 passengers and crew, but up to 16 passengers survived, including an 18-month-old boy shielded in his mother's arms, officials said.
Firefighters struggled to put out the blaze, which engulfed dozens of houses and at least 10 cars, but were assisted by a midmorning rain shower.
Transportation Minister Rajasa was quoted by the private Detik.com news Web site as saying 47 people on the ground were among the dead. City hospitals also were treating at least a dozen residents.
The plane crashed a minute after take-off at 10am (0300 GMT) on Monday from Medan city in northern Sumatra, Aljazeera's correspondent in Indonesia, Suhaib Jassim, reported.
Rising toll predicted
The toll may rise as the crash area is heavily populated, Jassim reported.
Some residents of the area, whose houses are just 500m from the airport, were killed, Jassim said.
Aljazeera learned that the governor of northern Sumatra province, some of his aides and a parliament representative from Medan were all killed in the crash.
Forty-seven people on the ground
are reported to have died
Foul play was highly unlikely, said the airline's managing
director Asril Tanjung, adding that human error or
technical failure may have been to blame.
The Boeing 737-200 was operated by Mandala, a low-cost carrier, and was heading to Jakarta when it crashed into a crowded housing complex, a witness, Rizal, told Metro television station.
"It happened very fast; no one even had time to panic," survivor Rohadi Kamsah Sitepu, 35, said from his hospital bed. "There was an explosion outside the plane followed by huge flames inside the cabin. Then we crashed."
"I struggled to take off my seat belt and then ran through a hole in the fuselage, jumping over charred bodies scattered all over the road," said Sitepu, who escaped with minor bruises to his legs. "It's a miracle I survived. I can't believe it."
The plane crashed into a crowded
The airport in Medan, the largest city on Sumatra island, is close to the centre of town and is surrounded by densely populated residential areas.
Indonesia's last crash involving a jetliner occurred in February, when 26 people were killed when a plane operated by Lion Air, another low-cost carrier, skidded off the runway on Java Island.
Mandala, which is partly owned by the military, has recently slashed the number of flights it operates to stay in business amid aggressive competition by newer airlines.
Many of its planes are more than 10 years old.